New answers tagged tiling
2
Here is a partial answer. It proves a fault-free rectangle can be assembled from rectangles of size mxn such that one dimension is not a multiple of the other.
The remaining cases can be converted to the 1xn case solved earlier by Bubbler.
4
Using Jaap's interpretation of the problem, I believe
First claim:
Proof by example:
Second claim:
Informal proof (might have a flaw):
A lemma is needed at this point:
Proof:
Back to the second claim:
As a demonstration of the construction, here are 2×5 tiles covering a 30×22 rectangle and 3×4 tiles covering a 36×27 rectangle, "seamlessly". ...
2
I left the empty square at A1. I found 25000 tilings that work for A1, out of an estimated 500 000 give or take a few hundred thousand.
The rectangles are marked with lighter colours.
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